9 Formally, a (one-tape) Turing machine is usually defined as a6-tuple M = (Q, Γ, s, b, F, δ), whereQ is a finite set of statesΓ is a finite set of the tape alphabet is the initial state is the blank symbol (the only symbol allowed to occuron the tape infinitely often at any step during thecomputation) is the set of final or accepting states is a partial function called the transition function, where L is left shift, R is right shift.

25 The Theory The Quantum AutomatonA quantum mechanical system can be conceptually designed, that we call quantum automaton, which has the following properties:it is endowed with mechanisms input and output of information,it can measure and record a variety of physical observables(including some of itself);it has an internal program that it can operate (once more according tothe laws of quantum mechanics) which includes a set of rules forpredicting the behavior of the measured physical systems (includingitself);its states, which are vectors in a Hilbert space and encode all thefeatures of the automaton (coding what is can measure, know,predict about itself and the external systems) are solutions ofquantum mechanical equations of motion; and all its measurableproperties correspond to some hermitian operator in that space.

26 An example: DNA replicationThe system wave-function will evolve to incorporate both the correctbase C for and the reverse base T for , whererefers to the state for which proton has not tunneled, andto that in which the proton did tunnel[ ] .The daughter DNA strand will be described by the wave function( )that will evolve as the coding strand is transcribed and translated in amutated form containing e.g an arginine ( ) histidine ( )amino acid substitution. The cell will thus move to statethat results in a different reading (e.g. due to the formation of lactose, ) of the automaton, while the cell ends up in superposition state

27 The ApplicationIf a particular gene has a role in some disease, and the genetic codeof that gene is known, one could use this knowledge to stop that genespecifically. Genes are made of double-helical DNA. When a gene isturned on, the genetic code in that segment of DNA is copied out as asingle strand of RNA, called messenger RNA. The messenger RNA iscalled a "sense" sequence, because it can be translated into a string ofamino acids to form a protein. The opposite strand in a DNA doublehelix (A opposite T, T opposite A, C opposite G, G opposite C) iscalled the "antisense" strand.The antisense coding sequence of a disease gene can be used to makeshort antisense DNAs in laboratory acting as drugs which work bybinding to messenger RNAs from disease genes, so that the geneticcode in the RNA cannot be read, stopping the production of thedisease-causing protein.